typical rise time(10% to 90%) is 2 microseconds, fall time to 50% is 50
microseconds.

It's also complex, with changes in amplitude and usually consists of
multiple closely spaced strikes appearing as one flash that might flicker
a bit. It may even have several distinct separate flashes.

Even if the stroke were always in the same direction the rapid varying
amplitude would make it basically an AC signal. If you pick the mean
current and then measure either side you will see substantial voltage
swings which would be positive and negative in reference to that point.

Taking the square wave of short duration. Tom remembers this stuff much
better than I so he may need to expand (or correct).

The theory part is a tad confusing as a perfect square wave consists of an
infinite series of harmonics. If that sounds confusing you should try to
figure the band width of a network signal which is basically DC. Yet,
it's DC only in the sense that it stays positive (I believe it's positive)
in reference to the common, or return path. The faster the rise time, or
fall time the broader the signal. Remember even CW is not zero band width
but depends on the sending speed as well as the characters being sent.

More that the bandwidth depends on the rise and fall time of the keying
waveform, as well as the sending speed.

The power for the perfect square wave would be a summation of an infinite
series, but in real life the lightening is a far cry from a perfect square
wave. In that case the power is basically a summation with some limit and
the power drops off at a given rate with frequency.

Even square waves have decreasing power for odd harmonics. A sawtooth
(which is a better representation of a lightning stroke) has decreasing
power for ALL harmonics. But, a harmonic representation is not a very good
one for lightning.

You've essentially got a single shot impulse here, so you probably don't
want to use a harmonic series representation.

With the miracle of modern computation.. I built a waveform some 131072
samples long, sampled at 1 nSec intervals, for a 1.5/50 microsecond
impulse, then calculated the power spectrum. Most of the power is down
quite low. By the time you get to even 1 MHz, you're already 60 dB down.

It's important to NOT confuse the spectral characteristics of the actual
stroke current with the spectral characteristics of signals that may be
induced by an adjacent stroke, or with the spectrum of the field radiated
by the stroke a long way away.

The RF emissions (radiated) from the stroke does have a significant
components well up into the tens of MHz. Partly because the "antenna" (i.e.
the lightning stroke itself) is bigger (in wavelength terms) for higher
frequencies. Sure, the lightning stroke has a huge amount of power down at
10kHz, but it's also a pretty poor antenna for that frequency. It's a
positively giant antenna for 20MHz or 50 MHz. There are also some
interesting spectral components coming from the stepped nature of the
typical lightning stroke.

If you make a simple approximation and put in a 20dB/decade correction, the
power vs frequency drops smoothly down to about -10dB at 1 MHz, sort of
asymptotically converging to around -14dB from 3-4 MHz on out. This is all
relative to a +50dB for DC (the dominant component) The analysis had
frequency bins about 7kHz wide.

And, when it comes to induced currents, it gets even more complex. Then
you have to take into account the frequency selectivity of the "victim
circuit".